If y = ² ≤ft( ^{-1} {1+x/1-x} ) , then dy/dx =

Correct Answer is : −12-1/22−1

Correct Answer is : −12-1/22−1

Test Index

AP EAMCET Engineering 21 Apr 2019 Shift 2 Paper

Section: Mathematics

Question : 66 of 160

Marks: +1, -0

If y =

\sin^2 \left( \cot^{-1} \sqrt{\frac{1+x}{1-x}} \right)

\frac{dy}{dx}

Solution:

The equation is given as,

y=\sin^2 \left( \cot^{-1} \sqrt{\frac{1+x}{1-x}} \right)

Substitute

x = \cos 2\theta \cdots (I)

y=\sin^2 \left( \cot^{-1} \sqrt{\frac{1+\cos 2\theta}{1-\cos 2\theta}} \right)

y=\sin^2 \left( \cot^{-1} \sqrt{\frac{2\cos^2\theta}{2\sin^2\theta}} \right)

y = \sin^2 (\cot^{-1} (\cot \theta))

y = \sin^2 \theta \cdots (II)

Differentiate the above equation with respect

\theta

\frac{dy}{d\theta} = 2 \sin \theta \cos \theta

\frac{dy}{d\theta} = \sin 2\theta \cdots (III)

Differentiate the above equation (I) with respect

\theta

\frac{dx}{d\theta} = -2 \sin 2\theta \cdots (IV)

From equation (III) and (IV)

\frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}} = \frac{\sin 2\theta}{-2 \sin 2\theta}

\frac{dy}{dx} = \frac{-1}{2}

Go to Question:

Prev Question

Next Question